Question

derivative problem:
f(x)= sec(x^2) find f'(sqrt(pi/4))
can someone explain how to do this?

Answer 1

The derivative of sec(x) is sec(x)tan(x)
Because it's sec(x^2) you use the chain rule to get the derivative as:
f'(x)=sec(x^2)tan(x^2) times (2x)

Then you plug in sqrt(pi/4) everywhere there's an x to find your answer.

Answer 2

How come you have to multiply the sec(x^2)tan(x^2) by the derivative of x^2 ?

Answer 3

The chain rule for derivation.

Answer 4

For example:
if f(x) = (2x)^5

2x is also a function and will need to be taken the derivative of.

f'(x) = 5(2x)^4 * (2)

5(2x)^4 because of the power rule of derivatives, and 2 because that's the derivative of the inner function.

Answer 5

okay thank you so much!

Answer 6

:)